Finite Group Databasebeta

← #14908359

Subgroups — #14908359

Order 2816.

656 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622521C211yesmaximal, characteristic, complemented
2#13078336C211yesmaximal, characteristic, complemented
3C2×#10622755C211yesmaximal, characteristic, complemented
4#13070746C214yesmaximal, complemented
5#13070736C214yesmaximal, complemented
6#13070411C211yesmaximal, characteristic, complemented
7#13070366C211yesmaximal, characteristic, complemented
8C2×#10622154C211yesmaximal, characteristic, complemented
9C11×#3407C211yesmaximal, characteristic, complemented
10C2×C11×#131C2211yescharacteristic
11#10623353—21no—
12C2×#67002—21no—
13C2×#66957C2211yescharacteristic
14C22×D88C2211yescharacteristic
15C11×#504—22no—
16C11×#504C2214yescomplemented
17C2×C11×M32—22no—
18C2×C11×M32C2211yescharacteristic
19C2×C11×M32C2211yescharacteristic
20#10622756C2212yescomplemented
21#10622755—22no—
22#10622755C2214yes—
23#10622755C2212yescomplemented
24#10622754—22no—
25#10622745—21no—
26C2×#66887—21no—
27C2×#66883C2211yescharacteristic
28C2×#66883C2211yescharacteristic
29#10622521—22no—
30#10622521—22no—
31C2×#66864C2212yescomplemented
32C2×D176C2212yescomplemented
33#10622155C2212yescomplemented
34#10622154C2214yescomplemented
35#10622154C2212yescomplemented
36#10622144C2214yescomplemented
37C2×C11×#41D411yescharacteristic
38C2×#4339—21no—
39C22×D44—21no—
40C11×#131—21no—
41C11×#131—21no—
42C11×#131D412yes—
43C11×#131C2312yes—
44C2×C11×M16—21no—
45C2×C11×M16D411yescharacteristic
46C22×C8×C11—21no—
47C22×C8×C11C2311yescharacteristic
48#67004—22no—
49#67003—42no—
50#67002—22no—
51#67002—24no—
52#67002—42no—
53#66995—41no—
54C2×#4325—41no—
55#66985—41no—
56C2×#4323—41no—
57C2×#4318—21no—
58C2×#4318—21no—
59C2×Dic44C2311yescharacteristic
60#66957—21no—
61#66957—21no—
62#66957—21no—
63#66957—21no—
64C2×D88—21no—
65C2×D88—21no—
66C2×D88—21no—
67C2×D88—21no—
68C2×D88—21no—
69C2×D88C2312yes—
70C2×D88C2311yescharacteristic
71C2×#4314—21no—
72C11×M32—21no—
73C11×M32—24no—
74C11×M32D412yes—
75C11×M32D412yes—
76C11×M32C2312yes—
77C2×C11×C16—21no—
78C2×C11×C16—24no—
79C2×C11×C16C2312yes—
80#66888—22no—
81#66887—24no—
82#66887—22no—
83#66883—21no—
84#66883—21no—
85#66883C2312yes—
86#66883C2312yes—
87#66864—24no—
88D176—24no—
89#33618—111nomaximal, Sylow
90C23×D11—41no—
91C11×#41—21no—
92C11×#41—21no—
93C11×#41D812yes—
94C11×#41C2×D412yes—
95C2×Q8×C11D811yescharacteristic
96C2×D4×C11—21no—
97C2×D4×C11D811yescharacteristic
98C22×C4×C11—21no—
99C22×C4×C11C2×D411yescharacteristic
100C2×C22⋊D11—41no—
101#4339—41no—
102#4339—41no—
103#4339—41no—
104#4339—41no—
105C2×D44—21no—
106C2×D44—22no—
107C2×D44—41no—
108C2×D44—41no—
109C2×D44—41no—
110C2×D44—41no—
111C2×D44—41no—
112C2×C4×D11—41no—
113C2×Dic22—21no—
114C11×M16—22no—
115C11×M16—22no—
116C11×M16—21no—
117C11×M16C2×D412yes—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11—21no—
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11C2×D411yescharacteristic
124C2×C8×C11#4111yescharacteristic
125C2×C8×C11#4111yescharacteristic
126C2×C8×C11C2411yescharacteristic
127#4326—42no—
128#4325—44no—
129#4325—42no—
130#4324—42no—
131#4323—44no—
132#4323—42no—
133#4318—22no—
134#4318—22no—
135#4318—41no—
136#4318—41no—
137C2×C11⋊C8—41no—
138C2×C11⋊C8—41no—
139Dic44—21no—
140Dic44—21no—
141D88—21no—
142D88—22no—
143D88—22no—
144D88—21no—
145D88—41no—
146D88—41no—
147#4314—41no—
148#4314—41no—
149C11×C16—22no—
150C11×C16C2×D414yes—
151C2×#509—111no—
152#3407D1111yescharacteristic, complemented
153#3067—111no—
154C2×#472—111no—
155#2223—114no—
156#2221—114no—
157#2161—111no—
158#2148—111no—
159C2×#361—111no—
160C23×C11—21no—
161C23×C11#13511yescharacteristic
162C22×D11—41no—
163C22×D11—42no—
164C22×D11—81no—
165C22×D11—81no—
166C22×D11—162no—
167Q8×C11—21no—
168Q8×C11C2×D812yes—
169D4×C11—22no—
170D4×C11—22no—
171D4×C11—21no—
172D4×C11C2×D812yes—
173C2×C4×C11—21no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11C2×D811yescharacteristic
179C2×C4×C11C2×D811yescharacteristic
180C2×C4×C11#13511yescharacteristic
181C2×C4×C11C22×D411yescharacteristic
182C22⋊D11—81no—
183C22⋊D11—81no—
184C2×Dic11—41no—
185D44—41no—
186D44—42no—
187D44—42no—
188D44—41no—
189D44—81no—
190D44—81no—
191C4×D11—81no—
192C4×D11—81no—
193Dic22—41no—
194Dic22—41no—
195C8×C11—22no—
196C8×C11#12111yescharacteristic
197C8×C11#12111yescharacteristic
198C8×C11C22×D411yescharacteristic
199C8×C11C2×#4111yescharacteristic
200C11⋊C8—42no—
201C11⋊C8—42no—
202#575—221no—
203C2×AGL(1,ℤ/8)—221no—
204C2×#135—111no—
205C22×D8—111no—
206C2×#131C2×D1111yescharacteristic
207#509—222no—
208#509—222no—
209C2×SD32—112no—
210C2×D16—112no—
211#504—22no—
212#504C2×D1114yescomplemented
213C2×M32—22no—
214C2×M32C2×D1111yescharacteristic
215C2×M32C2×D1111yescharacteristic
216#473—112no—
217#472—114no—
218#472—112no—
219#472—222no—
220#471—222no—
221C2×#108—111no—
222C2×#108—111no—
223#413—221no—
224C2×#100—221no—
225#368—114no—
226#362—112no—
227#361—114no—
228#361—112no—
229C22×C11—22no—
230C22×C11—41no—
231C22×C11—81no—
232C22×C11#46611yescharacteristic
233C22×C11#46611yescharacteristic
234C22×C11C2×#13511yescharacteristic
235C2×D11—82no—
236C2×D11—81no—
237C2×D11—162no—
238C2×D11—162no—
239C2×D11—161no—
240C2×D11—162no—
241C4×C11—22no—
242C4×C11#46611yescharacteristic
243C4×C11#46611yescharacteristic
244C4×C11C2×#12111yescharacteristic
245C4×C11C22×D811yescharacteristic
246Dic11—81no—
247C2×#41—221no—
248C2×#41D4411yescharacteristic
249C22×D4—221no—
250#137—222no—
251#137—441no—
252AGL(1,ℤ/8)—224no—
253AGL(1,ℤ/8)—222no—
254AGL(1,ℤ/8)—442no—
255AGL(1,ℤ/8)—441no—
256#135—221no—
257#135—221no—
258#135—221no—
259#135—221no—
260#135—442no—
261C2×Q16—111no—
262C2×SD16—221no—
263C2×SD16—441no—
264C2×D8—112no—
265C2×D8—111no—
266C2×D8—221no—
267C2×D8—221no—
268C2×D8—221no—
269C2×D8—221no—
270C2×D8—221no—
271C2×D8—441no—
272#131—21no—
273#131—21no—
274#131D4412yes—
275#131C22×D1112yes—
276C2×M16—21no—
277C2×M16—221no—
278C2×M16—221no—
279C2×M16D4411yescharacteristic
280C22×C8—21no—
281C22×C8C22×D1111yescharacteristic
282SD32—224no—
283D16—224no—
284M32—21no—
285M32—24no—
286M32C22⋊D1112yes—
287M32C22⋊D1112yes—
288M32C22×D1112yes—
289C2×C16—21no—
290C2×C16—24no—
291C2×C16C22×D1112yes—
292#108—112no—
293#108—112no—
294#108—221no—
295#108—221no—
296#101—222no—
297#100—224no—
298#100—222no—
299C2×C11—21no—
300C2×C11—21no—
301C2×C11—21no—
302C2×C11—42no—
303C2×C11C2×#46611yescharacteristic
304D11—161no—
305D11—162no—
306C24—441no—
307#41—21no—
308#41—21no—
309#41—441no—
310#41—441no—
311#41—441no—
312#41—441no—
313#41D8812yes—
314#41C2×D4412yes—
315C2×Q8—221no—
316C2×Q8D8811yescharacteristic
317C2×D4—21no—
318C2×D4—222no—
319C2×D4—221no—
320C2×D4—441no—
321C2×D4—441no—
322C2×D4—441no—
323C2×D4—441no—
324C2×D4—441no—
325C2×D4—441no—
326C2×D4D8811yescharacteristic
327C22×C4—21no—
328C22×C4—441no—
329C22×C4C2×D4411yescharacteristic
330Q16—221no—
331Q16—221no—
332Q16—442no—
333SD16—444no—
334SD16—442no—
335SD16—442no—
336SD16—441no—
337SD16—441no—
338D8—222no—
339D8—221no—
340D8—221no—
341D8—222no—
342D8—444no—
343D8—442no—
344D8—441no—
345D8—441no—
346M16—21no—
347M16—22no—
348M16—22no—
349M16—222no—
350M16—222no—
351M16—441no—
352M16—441no—
353M16C2×D4412yes—
354C2×C8—21no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—441no—
358C2×C8—441no—
359C2×C8C2×D4411yescharacteristic
360C2×C8#433911yescharacteristic
361C2×C8#433911yescharacteristic
362C2×C8C2×C22⋊D1111yescharacteristic
363C2×C8C2×C22⋊D1111yescharacteristic
364C2×C8C23×D1111yescharacteristic
365C16—22no—
366C16C2×C22⋊D1114yes—
367C11#3361811yescharacteristic, complemented, Sylow
368C23—21no—
369C23—441no—
370C23—442no—
371C23—881no—
372C23—881no—
373C23—1762no—
374C23#6695711yescharacteristic
375Q8—21no—
376Q8—441no—
377Q8—441no—
378Q8C2×D8812yes—
379D4—22no—
380D4—22no—
381D4—21no—
382D4—442no—
383D4—441no—
384D4—442no—
385D4—441no—
386D4—881no—
387D4—881no—
388D4—881no—
389D4—881no—
390D4C2×D8812yes—
391C2×C4—21no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—441no—
395C2×C4—881no—
396C2×C4—881no—
397C2×C4C2×D8811yescharacteristic
398C2×C4C2×D8811yescharacteristic
399C2×C4#6695711yescharacteristic
400C2×C4#6698311yescharacteristic
401C2×C4#6698311yescharacteristic
402C2×C4C22×D4411yescharacteristic
403C8—22no—
404C8—442no—
405C8—442no—
406C8#6698311yescharacteristic
407C8#6698311yescharacteristic
408C8C2×#433911yescharacteristic
409C8C22×C22⋊D1111yescharacteristic
410C22—22no—
411C22—41no—
412C22—81no—
413C22—881no—
414C22—882no—
415C22—1762no—
416C22—1761no—
417C22—1762no—
418C22—1762no—
419C22#1062272811yescharacteristic
420C22#1062272811yescharacteristic
421C22C2×#6695711yescharacteristic
422C4—22no—
423C4—881no—
424C4#1062272811yescharacteristic
425C4#1062272811yescharacteristic
426C4C22×D8811yescharacteristic
427C4C2×#6698311yescharacteristic
428C2—21no—
429C2—21no—
430C2—21no—
431C2—42no—
432C2—1762no—
433C2—1761no—
434C2C2×#1062272811yescharacteristic
subgroupG/H
centerC2C2×#10622728
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3407C2
socleC2×C11C2×#466
hypercenter#3407D11
hypocenterC11#33618
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#131 ◁ #3407

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#10622521C2semidirect
2. #13078336C2semidirect
3. C2×#10622755C2semidirect
4. #13070746C2semidirect
5. #13070736C2semidirect
6. #13070411C2semidirect
7. #13070366C2semidirect
8. C2×#10622154C2semidirect
9. C11×#3407C2semidirect
16. C11×#504C22semidirect
20. #10622756C22semidirect
23. #10622755C22semidirect
31. C2×#66864C22semidirect
32. C2×D176C22semidirect
33. #10622155C22semidirect
34. #10622154C22semidirect
35. #10622154C22semidirect
36. #10622144C22semidirect
152. #3407D11semidirect
212. #504C2×D11semidirect
367. C11#33618semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106225212
#130783362
C2×#106227552
#130707462
#130707362
#130704112
#130703662
C2×#106221542
C11×#34072
#3361811